In rectilinear MRI (Magnetic Resonance Imaging) acquisition, k-space data are typically acquired while a constant amplitude read gradient is applied. This results in a straight line trajectory during data sampling intervals. For example, in FIG. 2, the five straight lines of black dots 210 represent five sampling trajectories used to sample k-space data points using conventional rectilinear acquisition. In this type of rectilinear acquisition, the scan time is equal to TR (repetition time) times the number of phase encoding lines. For example, on the left side of FIG. 2, data is acquired using five read gradients and thus the acquisition time would be TR times five. In this conventional system, attempts to reduce scan time have included reducing the number of read phases by increasing the phase encoding step size. However, these approaches have typically lead to aliasing artifacts.